calculus question

Question

 

Find the area that is outside r = 2 but inside r = 4 cos θ.

Type your answer in the space below and give 3 decimal places. If your answer is less than 1, place a leading "0" before the decimal point (ex: 0.482)

Answer 1

^{Set both equations equal to each other. 2=4cos(θ) θ=π/3 or 5π/3. θ=π/3 is the first place both graphs will meet. Integrating the difference of the areas of the functions from θ=0 to θ=π/3 and then doubling this area will give you the area you are looking for.}

^{You want to integrate from θ=0 to θ=π/3 2 * 1/2 Integral[ (4*cosθ)^2 -2^2 dθ]}

^=7.65